English

Restricted extension of sparse partial edge colorings of hypercubes

Combinatorics 2017-11-06 v1

Abstract

We consider the following type of question: Given a partial proper dd-edge coloring of the dd-dimensional hypercube QdQ_d, and lists of allowed colors for the non-colored edges of QdQ_d,can we extend the partial coloring to a proper dd-edge coloring using only colors from the lists? We prove that this question has a positive answer in the case when both the partial coloring and the color lists satisfy certain sparsity conditions.

Keywords

Cite

@article{arxiv.1711.01073,
  title  = {Restricted extension of sparse partial edge colorings of hypercubes},
  author = {C. J Casselgren and K. Markström and L. A. Pham},
  journal= {arXiv preprint arXiv:1711.01073},
  year   = {2017}
}